Dov Monderer and Lloyd S. Shapley (1996), Games and Economic Behavior 14(1):124–143, DOI-10.1006/game.1996.0044
Key takeaways
Registered, not read. What follows comes from papers that restate it. None of it is checked against the paper.
- Four kinds of potential. An exact potential is a real function φ on strategy profiles whose change, when one player deviates, equals that player’s change in payoff. Candogan et al. (LIT-1442, Definition 2.1, p. 6) give this definition and credit it to this paper. A weighted potential matches each player’s payoff change up to a positive player-specific weight. An ordinal potential matches its sign. A generalized ordinal potential need only rise whenever the deviating player’s payoff strictly rises. Every restatement read gives each of these as a real-valued function.
- The finite improvement property (FIP). An improvement path is a sequence of profiles in which each step is a strict unilateral improvement by the player who moves. A game has the FIP if every such path is finite. Duersch, Oechssler and Schipper (arXiv 1003.4274, p. 18 of the arXiv PDF) report: “Monderer and Shapley (1996, Lemma 2.5) show that a finite strategic game has no strict improvement cycle (what they call the finite improvement property) if and only if it is a generalized ordinal potential game.” Biggar and Shames (arXiv 2502.03546, p. 18) report it more weakly: “Monderer and Shapley (1996b) show that ordinal potential games satisfy the ‘finite improvement property’”. The lemma’s exact wording, number and page are therefore not confirmed.
- Equilibria and dynamics. Candogan et al. restate as their Theorem 5.2, citing this paper, that a potential game has the same equilibria as the game in which every player’s payoff is the potential, and so has a pure Nash equilibrium (p. 22). They also say that fictitious play and best-response dynamics “converges in potential games”, citing this paper among others (p. 23).
Standing in the record
Filed on 2026-10-23 at the owner’s request, as the source of the formal sense of “potential” that the record is adopting for “an ordering prevails in the negotiation among a system’s perspectives” (TERM-076, CLAIM-440, QUESTION-268). THEORY-896 states the FIP equivalence for finite games and proves it in the record, so the result does not wait on this copy. Its attribution, wording and numbering do.